Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001651
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001651: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1},{2}}
 => [1,2] => ([(0,1)],2)
 => ([(0,1)],2)
 => 0
{{1,2,3}}
 => [2,3,1] => ([(1,2)],3)
 => ([(0,1)],2)
 => 0
{{1},{2},{3}}
 => [1,2,3] => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
{{1,2,3,4}}
 => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => 1
{{1,2,3},{4}}
 => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 0
{{1,2},{3,4}}
 => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 0
{{1,3},{2,4}}
 => [3,4,1,2] => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
{{1},{2,3,4}}
 => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => 0
{{1,4},{2},{3}}
 => [4,2,3,1] => ([(2,3)],4)
 => ([(0,1)],2)
 => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
{{1,2,3,4,5}}
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 1
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => 1
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => 0
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => ([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => 1
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,1)],2)
 => 0
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => ([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => 0
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => 0
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => ([(0,4),(1,2),(1,3)],5)
 => ([(0,1)],2)
 => 0
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => ([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 1
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 3
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 0
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 0
{{1,5},{2,3,4}}
 => [5,3,4,2,1] => ([(3,4)],5)
 => ([(0,1)],2)
 => 0
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => 1
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1)],2)
 => 0
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 0
{{1,4,5},{2},{3}}
 => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 0
{{1,4},{2,5},{3}}
 => [4,5,3,1,2] => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
{{1,4},{2},{3},{5}}
 => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 0
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,1)],2)
 => 0
{{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => ([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 1
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => 0
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 3
{{1,2,3,4,5,6}}
 => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 3
{{1,2,3,4,5},{6}}
 => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
{{1,2,3,4},{5,6}}
 => [2,3,4,1,6,5] => ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
{{1,2,3,4},{5},{6}}
 => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ([(0,2),(2,1)],3)
 => 1
{{1,2,3,5},{4,6}}
 => [2,3,5,6,1,4] => ([(0,5),(1,4),(3,2),(4,3),(4,5)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 2
{{1,2,3},{4,5,6}}
 => [2,3,1,5,6,4] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 2
{{1,2,3},{4,5},{6}}
 => [2,3,1,5,4,6] => ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => ([(0,2),(2,1)],3)
 => 1
{{1,2,3,6},{4},{5}}
 => [2,3,6,4,5,1] => ([(1,5),(4,3),(5,2),(5,4)],6)
 => ([(0,1)],2)
 => 0
{{1,2,3},{4},{5,6}}
 => [2,3,1,4,6,5] => ([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
 => ([(0,2),(2,1)],3)
 => 1
{{1,2,3},{4},{5},{6}}
 => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ([(0,1)],2)
 => 0
{{1,2,4,5},{3,6}}
 => [2,4,6,5,1,3] => ([(0,5),(1,4),(1,5),(4,2),(4,3)],6)
 => ([(0,1)],2)
 => 0
{{1,2,4,6},{3,5}}
 => [2,4,5,6,3,1] => ([(1,3),(1,5),(4,2),(5,4)],6)
 => ([(0,2),(2,1)],3)
 => 1
{{1,2,4},{3,5,6}}
 => [2,4,5,1,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 4
Description
The Frankl number of a lattice. For a lattice $L$ on at least two elements, this is $$ \max_x(|L|-2|[x, 1]|), $$ where we maximize over all join irreducible elements and $[x, 1]$ denotes the interval from $x$ to the top element. Frankl's conjecture asserts that this number is non-negative, and zero if and only if $L$ is a Boolean lattice.